S. Eisenmann, Y. Katzir, A. Zigler
G. Fibich, Y. Sivan
Israel
J. Penano, P. Sprangle
Hebrew University, Jerusalem, Israel
Tel Aviv University, Tel Aviv,
Navy Research Lab. Washington DC, USA
FRISNO 2009, Feb. 13st, Ein Gedi
Terawatt laser pulses propagate in the atmosphere over many
diffraction lengths without diverging.
Kerr Self-focusing
P > Pcr ~ 4 GW
nonlinear contribution
to refractive index
Free propagation of a
1 TW laser pulse.
Terawatt laser pulses propagate in the atmosphere over many
diffraction lengths without diverging.
d0~100μm
Intensity is sufficient to ionize air
molecules through MPI (Up~ 12 eV)
I=1012 – 1014 W/cm2
Terawatt laser pulses propagate in the atmosphere over many
diffraction lengths without diverging.
I=1012 – 1014 W/cm2
d0~100μm
Terawatt laser pulses propagate in the atmosphere over many
diffraction lengths without diverging.
A dynamic balance between
nonlinear focusing and plasma defocusing
will create a filament
d0~100μm
I=1012 – 1014 W/cm2
n = n0 + n2 I (r ) − ne (r ) / 2nc
Terawatt laser pulses propagate in the atmosphere over many
diffraction lengths without diverging.
Applications:
- Remote sensing
- Lightning control
- Microwave guiding
- THz generation
- Remote LIBS
Stages in propagation of a high power beam in air
Standard view:
ƒ A pulse with input power P >> Pcr (~ 4 GW in air) selffocuses and typically collapses after 5-20 meters
ƒ
After the collapse, non-diffracting plasma filaments are created
(length > 10 m)
ƒ
Filaments decay due to plasma absorption
Stages in propagation of a high power beam in air
In this talk:
ƒ
Controlling filamentation pattern
ƒ
Delaying filamentation collapse
ƒ
Monitoring the fine structure of plasma
filaments
ƒ
Plasma effect on termination of filaments
Terawatt (P>>Pcr) pulses break up to multiple filaments (MF).
1.5 TW (τ=55 fsec, λ=0.8 μm) pulse
Can we control MF ?
ƒ
Input beam noise initiates the beam
filamentation
ƒ
Straight forward approach: produce a clean(er) input beam
But this is not an easy task at these high powers.
ƒ
Our approach: Rather than fight noise, simply add large
controllable distortion.
ƒ
Advantage: easier to implement, especially at the powers used
for atmospheric propagation
ƒ
Usually noise breaks the symmetry randomly.
ƒ
By introducing elliptical symmetry we control the ‘allowed’
locations for filamentation:
ψ ∝e
r ≠ -r
− ( x2 / a 2 + y 2 / b2 )
x → -x, y → -y
Opt. Lett. 29, 1772 (2004)
Single shot
Average
1000 shots
320 shots , P=22Pcr , after 5 meters of propagation
STD of scatter:
X: 150 ± 40 μm
Y: 2000 ± 40 μm
X,Y: 60 ± 20 μm
Opt. Lett. 29, 1772 (2004)
A controllable amount of astigmatism can:
ƒ Create a shot to shot deterministic pattern
ƒ Reduce number of filaments
ƒ Reduce the filament scatter
320 shots , P=22Pcr , after 5 meters of propagation
STD values of scatter:
X: 150 ± 40 μm
Y: 2000 ± 40 μm
X,Y: 60 ± 20 μm
Opt. Lett. 29, 1772 (2004)
Mathematical model is complex:
• NLS: Diffraction + Kerr nonlinearity
• Normal GVD
• Plasma formation
• plasma defocusing
• plasma absorption
• Raman
• Self Steepening
…
0
zc
z
Mathematical model is complex:
• NLS: Diffraction + Kerr nonlinearity
• Normal GVD
• Plasma formation
• plasma defocusing
become important only
• plasma absorption
• Raman
after the collapse
• Self Steepening
…
0
zc
z
Until the collapse (0 ≤ z ≤ zc), atmospheric propagation is
governed by NLS with normal GVD (b2>0):
2
iAz ( z , x, y, t ) + ∇ A − b2 Att + A A = 0
2
⊥
0
zc
z
Standard approach is to add negative chirping to initial pulse:
an initially long (and weak) pulse compresses (gets shorter and stronger)
along the propagation.
Disadvantages of method:
ƒ Reduces the overall power at collapse point
ƒ Experimental results < 250 meters (Teramobile)
A new method is needed to reach kilometer range!
For “long pulses” (τ >25 fsec) : Ldisp >> zc
• Air GVD is also negligible
• Pre-collapse model reduces to the NLS
2
iAz ( z , x, y, t ) + ∇ A + A A = 0
2
⊥
0
zc
z
• Initially, linear defocusing.
defocusing
• Then, nonlinear self-focusing.
• Collapse is delayed: Zc Æ Zc(F) .
1
Z c( F )
1 1
=
+
Zc F
The “original” nonlinear collapse point, is mapped to a new location. Even though
the collapse point is dictated by the NLS the adjustment due to divergence is dictated
by the linear lens transformation (Talanov ’70).
• “Tunable defocusing lens” –
using a simple telescope setup.
• Control the collapse distance
by varying the distance, d
between the lenses.
Z c( F1 , F2 ) = d + F2
zc ( F1 − d ) − dF1
( F1 + F2 ) zc + F1 F2 − d ( zc + F1 )
• Achieved a 4-fold delay.
• With excellent fit to theory
Opt. Exp. 14 p. 4946 (2006)
• “Tunable defocusing lens” –
using a simple telescope setup.
• Control the collapse distance
by varying the distance, d
between the lenses.
Outdoor experiment
• Collapse delayed to 330 meters.
• Achieved a 20-fold delay.
• Results agree with theoretical
formula.
Opt. Exp. 15 p. 2779 (2007)
A localized filament pattern at a
distance of ~ 320 m
• No tilt: scatter area ~ 6 X 7 mm.
• With tilt: scatter area
four times smaller .
Filaments at 330 meters (30 sec integration)
Opt. Exp. 15 p. 2779 (2007)
Stages in propagation of a high power beam in air
Nonlinear Schrödinger eq:
2
iAz ( z , x, y, t ) + ∇ 2⊥ A − b2 Att + A A = 0
Leading term is: |A|2
Main Findings:
I. Introducing controlled distortion to beam Æ shot to shot stable filaments
II. A simple telescope setup can be easily used to control and delay collapse
Opt. Exp. 14 p. 4946 (2006) Opt. Exp. 15 p. 2779 (2007)
Stages in propagation of a high power beam in air
Things become much more complex ...
Kerr nonlinearity
GVD
Raman
Self Steepening
Ionization (absorption & defocusing)
ΓMPI ∝ A
2k
k =8 (number of photons for MPI)
In previous experiments preformed by various research groups the
measured electron densities vary:
−3
ne = 10 − 10 [cm ]
12
17
The measurements were spatially or temporally integrated.
F. Theberge et al., Phys. Rev. E 74, 036406 (2006)
A. Becker et al., Appl. Phys. B 73, 287 (2001)
H.D. Ladouceur et al., Opt. Commun. 189, 107 (2001)
S. Tzortzakis et al., Opt. Commun. 181, 123 (2000)
S. Tzortzakis et al., Phys. Rev. E 60, R3505 (1999)
B. La Fontaine et al., Phys. Plasmas 6, 1615 (1999)
B. La Fontaine et al., Phys. Plasmas 6, 1615 (1999)
H. Schillinger and R. Sauerbrey, Appl. Phys. B 68, 753 (1999)
Our control technique allows to track the fine structure
of a single plasma filament along the propagation axis
d = 1.5 mm
C = 1 nF
V = 0 – 5 kV
We monitor:
No filament
V0
h=
V fil
t
With filament
Along the plasma filament
t
PRL. 98, 155002 (2007)
1. We measured h in a controlled setup
without filamentation, for various
intensities of the beam between the
electrodes.
Initial relative electron density (a.u.)
calibration of h parameter
2. Ionization is predominantly due to MPI.
ΓMPI ∝ I k
PRL. 98, 155002 (2007)
A 228 GW, 100 fsec pulse was launched to the atmosphere.
It was focused & arranged using a f = 2 m lens.
I. Peak electron density ~ 5x1016 cm-3
II. Rapid electron density variation.
An order of magnitude change over a
distance of 5 cm.
III. Postionization regime –
Guided light structure supported by a
low electron density region (ne< 1015
cm-3).
As predicted theoretically (Champeaux & Berge 2005)
IV. Almost 3 orders of magnitude drop
in electron density over the entire
filament
PRL. 98, 155002 (2007)
More features are observed for various initial powers:
I. Highest electron density may be reached after filamentation onset
II. After “low ionization region” high electron densities may re-emerge
III. Postionization regime is seen always –
Guided light structure supported by a low electron density region
(ne< 1015 cm-3)
PRL. 98, 155002 (2007)
Full (3+1)D Simulation & Experiment
HELCAP code Æ PRE 66 046418 (2002)
Graph from Æ PRL 100 155003 (2008)
Full (3+1)D Simulation & Experiment
The formation of the initial filaments is very sensitive to the initial laser pulse field, i.e.,
both intensity and phase, which is likely to differ significantly between simulation and
experiment. This may account for the discrepancy in the microscale evolution of the
density between the simulation and experiment for z < 50 cm
HELCAP code Æ PRE 66 046418 (2002)
Graph from Æ PRL 100 155003 (2008)
Full 3D+1 Simulation & Experiment
As filamentation progresses the pulse loses energy and the plasma density decays. This
macroscopic decay of the plasma density is not strongly dependent on the evolution of
individual filament.
Good agreement between simulation and experiment with respect to the macroscopic
decay of the plasma density, as is evident for 50 < z <200
HELCAP code Æ PRE 66 046418 (2002)
PRL. 98, 155002 (2007)
Main findings:
I. Electron density in plasma channel is not constant – can vary over three
orders of magnitude
II. Rapid electron density variation. An order of magnitude change over a
distance of 5 cm (~ ½ diffraction length).
III. Assuming peak densities of 5x1016 cm-3 Æ Postionization regime:
Guided light structure supported by a low electron density region
(ne< 1015 cm-3)
IV. After “low ionization region” high electron densities may re-emerge
PRL. 98, 155002 (2007)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
I. Initially plasma is almost unchanged
II. Strong focusing
III. Plasma filament is terminated
Zoom
Free propagating
With pinhole
300 < z < 380
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
15 GW
P > 3 Pcr
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
15 GW
P > 3 Pcr
Even though P > Pcr the beam cannot refocus, this is due to
the fact plasma increases the effective power for self focusing.
⎡ 2
⎤
2πk
PSF ≈ ⎢ M +
r Rne 0 ⎥ Pcr ≈ 7 Pcr
2 e
(k + 1)
⎣
⎦
ne 0 − electron density
k − photon number
re − classical electron radius
R − filament radius
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
15 GW
P > 3 Pcr
Even though P > Pcr the beam cannot refocus, this is due to
the fact plasma increases the effective power for self focusing.
⎡ 2
⎤
2πk
PSF ≈ ⎢ M +
r Rne 0 ⎥ Pcr ≈ 7 Pcr
2 e
(k + 1)
⎣
⎦
ne 0 − electron density
k − photon number
re − classical electron radius
R − filament radius
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
15 GW
P > 3 Pcr
P < PSF
Even though P > Pcr the beam cannot refocus, this is due to
the fact plasma increases the effective power for self focusing.
⎡ 2
⎤
2πk
PSF ≈ ⎢ M +
r Rne 0 ⎥ Pcr ≈ 7 Pcr
2 e
(k + 1)
⎣
⎦
ne 0 − electron density
k − photon number
re − classical electron radius
R − filament radius
PRL. 100, 155003 (2008)
Effect of the background energy
We add a 500 μm pinhole (at z = 302 cm) and monitor the plasma
18 GW
P > 4 Pcr
15 GW
P > 3 Pcr
P < PSF
Main Findings:
I. Energy depletion due to ionization reduces the pulse power slightly
II. Plasma defocusing effectively increase the critical power for filamentation Æ
without re-boost from background energy filament will terminate
PRL. 100, 155003 (2008)
Controlling filamentation
I. Introducing controlled distortion to beam Æ shot to shot stable filaments
II. A simple telescope setup can be easily used to control and delay collapse
Plasma filament
II. Electron density in plasma channel is not constant – can vary over three
orders of magnitude
III. Rapid electron density variation. An order of magnitude change over a
distance of 5 cm.
IV. Assuming peak densities of 5x1016 cm-3 Æ Postionization regime:
Guided light structure supported by a low electron density region
(ne< 1015 cm-3)
V. After “low ionization region” high electron densities may re-emerge
Filament Termination
VI. Energy depletion due to ionization reduces the pulse power
VII. Plasma defocusing effectively increase the critical power for filamentation
Æ
without re boost from background energy filament will terminate
About this work & more filaments related:
• G. Fibich, S. Eisenmann, B. Ilan, A. Zigler
Optics Letters 29, p. 1772 (2004)
•
G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, A. Zigler
Optics Express 13, p. 5897 (2005)
• G. Fibich, Y. Sivan, Y. Erlich, E. Louzun, M. Fraenkel, S. Eisenmann, Y. Katzir, A. Zigler
Optics Express, 14 p. 4946 (2006)
• S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, G. Fibich
Optics Express 15, p. 2779 (2007)
• S. Eisenmann, A. Pukhov and A. Zigler
Physical Review Letters 98, 155002 (2007)
• S.Eisenmann, Joseph Penano, Philip Sprangle and A. Zigler
Physical Review Letters 100, 155003 (2008)
Thank you for your time
ICPSA2009, Feb. 1st, Jerusalem